A compound Poisson-Sujit framework for over-dispersed radiation monitoring data

This paper proposes a novel one-parameter discrete probability model, termed the Poisson–Sujit (PSJT) model, developed by compounding the classical Poisson distribution with the recently introduced Sujit (SJT) model. The resulting model offers improved flexibility for modeling count data by leveraging the analytical simplicity of the Poisson framework and the adaptability of the SJT distribution. A comprehensive theoretical analysis establishes key distributional characteristics, illustrating that an increase in the model's parameter leads to reductions in the mean, variance, and IQR, while the skewness exhibits an increasing trend. Parameter estimation is carried out using both the method of moments and maximum likelihood estimation techniques. To evaluate the statistical properties of the estimators, an extensive Monte Carlo simulation study is performed, indicating that the maximum likelihood method consistently provides greater accuracy and efficiency across a range of scenarios. The practical relevance of the PSJT distribution is demonstrated through its application to two empirical datasets: one related to cytogenetic damage analysis, and another involving dicentric chromosome counts in human peripheral blood following exposure to a 1.600 Gy dose of 1480 MeV oxygen ions. Comparative goodness-of-fit assessments confirm the superior fitting capability and interpretability of the PSJT model relative to existing alternative distributions.